Scissors Congruence for Certain k-polygons

It has been proved that any two polygons having the same area are scissors congruent by Bolyai in 1832 and by Gerwien in 1833, respectively. It is well known that the concepts of congruence and scissors congruence are different for the set of polygons in the Euclidean plane. Let C be a unit circle divided into n parts equally. We denote the set of ends of these parts on C by S = {P0; P1; : : : ; Pn􀀀1}. Let }k(n) be the set of all k-polygons inscribed in C, where the vertices are taken from S. In this paper, we shall investigate the relations of the concepts of congruence and scissors congruence in this special set of k-polygons }k(n).

2010 Mathematics Subject Classification. Primary10A45; Secondary 52B45